Geoscience Reference
In-Depth Information
Atmosphere
0.028
0.8
3.2
4.2
0.5
0.3
Surface ocean
138
Continental biota
1040
Marine
biota
3000
998
2710
18
58
42
63.5
63.5
Soils
Deep ocean
1.7
200 000
87 100
18.7
21.4
1.9
4 × 10
9
Sediments
Figure 6.6
The external cycle of phosphorus (Lerman,
1988
). Masses (solid type) and fluxes (grey tinted
type) are in millions of tons of phosphorus per year.
length of time compared with the relaxation time of the system. The phosphorus cycle is
One aspect of cycles that is difficult to grasp is that of the time scale at which they apply.
It is easy to see that estimating the transportation of an element to the ocean by rivers in
flood or from the mantle to the atmosphere by extrapolating from observation of a volcanic
eruption gives an inaccurate representation of flows. Catastrophic transfer (or pulse trans-
fer) is particularly difficult to fit into the picture. Another condition may seem implicit to
the idea of a cycle, that of the stationary state, or the balanced cycle: an atom is passed many
times through all of the reservoirs and the inventory of each reservoir no longer varies. This
condition is always an approximation to some extent. Suppose we are interested in the car-
bon cycle at appropriate time scales for historical climatic variations (100-2000 years).
Should we include all carbon transfers between the mantle, crust, ocean, atmosphere, and
biomass; and at all time scales, from diurnal (daily) rhythms of the biomass to fluctua-
tions of volcanic emission, at very long geological time scales? At the scale of a century,
the effect of diurnal fluctuation is that of the sum of 365
100 cycles and its effect is
therefore virtually nil. At the scale of a millennium, the long geological variations will be
tenuous. Adding that effect would be the same as arbitrarily introducing a transfer equa-
tion equivalent to “non information.” Now, it is well known in mathematics that adding
an equation of the type 0
×
0 makes a system of equations insoluble. To ensure the cycle
is described properly, we will therefore choose conservatively to draw up an inventory of
=
